A New Method for Generating the Design Matrix of a Linear Regression Model | ||||
| The Egyptian Statistical Journal | ||||
| Article 7, Volume 39, Issue 1, June 1995, Page 106-119 PDF (6.4 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.1995.314799 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| Adel M. Hallawa* 1; Abdul-Mordy H. Azzam2 | ||||
| 1Dep. of Statistics, Faculty of Economic and Administrative Sciences, United Arab Emirates University, Al-Ain, United Arab Emirates | ||||
| 2Faculty of Economics and Management, King Saud University, Saudi Arabia | ||||
| Abstract | ||||
| This paper introduces a new algorithm for generating the design matrix X, of a linear regression model, with prespecified simple correlation coefficients between each pair of its columns. Controlling the correlation coefficients among the regressors makes the proposed algorithm useful for simulation studies of biased estimation techniques under linear regression models where different degrees of multicollinearity have to be investigated to judge their performance. Unlike the existing algorithms, the new generated matrices have certain desirable features that will be discussed in the sequel. A small simulation study, reveals some differences between the results obtained from applying the new and the McDonald and Galarneau (1975) algorithms. Our main claim is that, the results associated with the new algorithm describe the true state of nature more precisely. | ||||
| Keywords | ||||
| Correlation Matrix; Positive Definite Matrices; Eigenvalues; Orthonormal Eigenvectors; Ridge Regression | ||||
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